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We implement the Maynard-Tao method of detecting primes in tuples to investigate small gaps between primes in arithmetic progressions, with bounds that are uniform over a range of moduli.
Let be an -tuple of positive, pairwise distinct integers. If for all the prime divisors of come from the same fixed set , then we call the -tuple -Diophantine. In this note we estimate the number of -Diophantine quadruples in terms of .
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